Solute transport in bounded porous media characterized by generalized sub-Gaussian log-conductivity distributions

Abstract

There are increasing evidences that probability distributions and associated statistical moments of a variety of hydrogeological and soil science variables and their spatial increments display distinctive scale-dependent features that are not captured by a typical Gaussian model. A Generalized Sub-Gaussian (GSG) model is able to capture key aspects of this pattern. We present the results of a suite of computational analyses set in a Monte Carlo framework and aimed at assessing the impact of a GSG structure of log hydraulic conductivity ( ) on transport of a conservative solute through a threedimensional bounded porous medium under steady-state saturated Darcy flow. Our results indicate that the longitudinal spreading of a plume is on average significantly smaller for Sub-Gaussian than for Gaussian Y fields. Otherwise, the velocity field arising from a Sub-Gaussian Y field induces enhanced plume stretching with respect to what can be observed in a Gaussian Y setting, this aspect potentially influencing the strength of solute mixing within these two types of conductivity domains. We also find that, in some cases, it may be difficult to identify the nature of the underlying conductivity field relying solely on observations of solute concentrations migrating within the system. In this regard, we show that the action of local dispersion tends to mask the influence of Sub-Gaussianity on major transport metrics.

Macrodispersion in generalized sub-Gaussian randomly heterogeneous porous media

“…In this study, we focus on the classical macrodispersive approach where the effect of system heterogeneity is addressed through the action of macrodispersion coefficients. The latter are conceptualized as attributes of the porous domain [1,3,12,17,18] in a way which is very similar to the case of thermal diffusivity. Thus, even as our study is keyed to mass transfer, the approach and strategy of analysis are readily transferable to settings entailing heat transfer in randomly heterogeneous porous media.…”

“…Libera et al [34] provide a first numerical study on the effect of a GSG distribution of Y on concentration breakthrough curves at a well operating in a two-dimensional system. More recently, the role of the GSG nature of Y on transport behavior has been explored in [18] through a detailed suite of numerical Monte Carlo simulations within a laboratory column. Analytical solutions depicting transport in two-dimensional GSG domains are presented in [32] and [19].…”

“…The intrinsic spatial variability of the attributes of the host porous medium (e.g., permeability and porosity of natural subsurface reservoirs) prevents obtaining general closed-form analytical solutions describing the dynamics of quantities of interest such as space-time distributions of solute concentration. uncertainty quantification typically rests on a Monte Carlo framework and entails the need for large collections/ensembles of realizations [11,13,18]. This is in turn associated with large computational costs which might be somehow demanding from a data management and practical perspectives.…”

Features of transport in non-Gaussian random porous systems

“…As expected, the difference between statistics of c(x, t) obtained with diverse α values decreases as the travel time increases and as Pe decreases (see also Figure 3.b). We point out that the effect of α on the concentration breakthrough curve (BTC) in a single realization of the permeability field has been investigated in the past [46,57]. In general, the authors observed that decreasing the value of α yields (i) a delayed first time of arrival of the solute and (b) an increasing degree of asymmetry (and heavier tails) of the BTC.…”

Emergence of non-Fickian transport in truncated pluri-Gaussian permeability fields

“…In this work we investigate solute transport and the onset of anomalous or non-Fickian transport behaviour in high-contrast heterogeneous permeability fields, generated with the geostatistical pluri-Gaussian truncated (PGS) method (Mariethoz et al 2009). Solute transport has been widely investigated in continuous Gaussian and non-Gaussian permeability fields (Gotovac et al 2009;Sole-Mari et al 2021), and methods have also been proposed to handle non-continuous fields, suitable to reproduce geomaterials where property transition is marked by sharp interfaces (Bianchi and Pedretti 2017). PGS random fields are used in this context to model actual subsurface geological media in a sedimentary setting.…”